86 replies to this topic

[Sip]

I can not stick to the problem, because Armat is talking about a specific paradox which has nothing to do with your interpretation.

That is why I made sure I clarified exactly what problem I was referring to. That is the ONLY way to prevent being a bonehead

[Twilight Bark]

Phew. Glad I didn't get involved in the hostilities. Also glad that the version of the ambiguous original problem I "solved" was not considered by any of the warring factions. Please leave it at that.

A few quick thoughts to add:

Since we are asked to choose "true" or "false" (or "other"), we are forced to start with taking the statement at face value ("true"). If the question were "I am a redhead", or any other simple assertion, the only reasonable answer would be "other" since we really don't know. But that's not in the spirit of the question. The fact that the statement was more complex does not detract from the necessity to start with the assumption that it is true. So, while it is perfectly reasonable to test two assumptions and see where they lead, the spirit of the question really dictates that we only start with assuming the statement to be true and see where it leads. The statement is true unless you prove it false. Or you may arrive at a paradox.

Which brings me to the second point. A paradox does not imply that the statement is false. It implies that the statement is useless (i.e. without any usable information). In terms of fuzzy logic, something that isn't true isn't necessarily false. And in terms of binary logic, a paradox isn't false per se; it's not even false, it's nonsense. I think this point might have been overlooked here.

[Twilight Bark]

“Those who speak, know nothing.”

Let’s assume that it is true.  Then the above speaker knows nothing, therefore he would not know what those who speak may know or not. Therefore, him/her being a speaker, that statement cannot be true.

... , that statement may or may not be true. Knowing nothing implies that he has no information. But even with no information he will be right half the time (about true-false problems).

.... Therefore, those who speak may know something.  This is the only valid implication of the quoted statement with absolutely no built-in paradoxical structure.

That conclusion (that the given statement is false in the strict sense) is correct, but not because of contradicting the initial assumption (which it does, and in the absence of other logical results, that would make it paradoxical, not false), but as a matter of simpler linear deduction.

I have a feeling that fuzzy logic experts would find a way to make it half-right (after all the statement is false not because we know for sure that those who speak may know something, but because we have no idea if they may or not).
But I won't go there.

[MJ]

... , that statement may or may not be true. Knowing nothing implies that he has no information. But even with no information he will be right half the time (about true-false problems).


That conclusion (that the given statement is false in the strict sense) is correct, but not because of contradicting the initial assumption (which it does, and in the absence of other logical results, that would make it paradoxical, not false), but as a matter of simpler linear deduction.

I have a feeling that fuzzy logic experts would find a way to make it half-right (after all the statement is false not because we know for sure that those who speak may know something, but because we have no idea if they may or not).
But I won't go there.

[Sasun]

Domino, breaking my head with a paradox? hmm... I doubt, my head is paradox-proof

[Twilight Bark]

That conclusion (that the given statement is false in the strict sense) is correct, but not because of contradicting the initial assumption (which it does, and in the absence of other logical results, that would make it paradoxical, not false), but as a matter of simpler linear deduction.

I have a feeling that fuzzy logic experts would find a way to make it half-right (after all the statement is false not because we know for sure that those who speak may know something, but because we have no idea if they may or not).
But I won't go there.  

Upon further reflection, I am not sure the statement "Those who speak know nothing" qualifies as "false" even under binary logic. It cannot be proven to be false. And it cannot be proven to be true. We appear to have decided in this thread that what is not proven to be true must be false. I don't think that's quite right. It's a statement whose truth cannot be determined. It's either a paradox or an "indeterminate" statement. In both cases it has a complete lack of information.

Those who speak know nothing --> I know nothing --> Those who speak may know something -->
--> Possibility 1: The speaker of the original statement knows something (paradox) (fuzzy truth value = 0.5)
--> Possibility 2: The speaker of the original statement knows nothing
--> Possibility 2.1: The original statement is true by chance (truth value = 0)
--> Possibility 2.2: The original statement is false by chance (truth value = 1)
--> Fuzzy truth value of Possibility 2 = (0+1)/2 = 0.5
---> Fuzzy truth value of the statement: (0.5+0.5)/2=0.5



I would like to end my contribution to this amusing thread (thanks Armat), by maintaining that it is important to distinguish falsehood from paradox, and to know why we regard something as not true (is it because we know it to be false, or is it that the statement is not justified but not necessarily false?). Failing to master those "niceties" allows us to be manipulated, or become unwitting participants in manipulation.

Even if we make mistakes in our logical process, the act of striving for logical judgement already makes us less prone to manipulation.

[Armat]

I got kick out of reading this thread again.
Kind of sad nobody much posts here anymore. During this thread 2003 wow this place was hot!